In problems 1-10, find the horizontal and vertical asymptotes of the graph of the function using algebraic techniques. You can use a graphing calculator to verify your answer, but not instead of the algebra. For #9 & 10, briefly describe in words why the functions have the asymptotes. f(x)=1/(x-2)^2
f(x)=1/x^3+3
f(x)=x^3-3x^2+5x-2
f(x) = x − 3/x + 3
f(x)=x^2/x^2-9
f(x)=1-x^2/x^2-2x+1
f(x)=x^2-4/x^4-16
f(x)=x(x-1)(x-2)/x^4-x^2
f(x)=e^x
f(x) = ln x
Find a function f(x), which has 2021 vertical asymptotes and 2 horizontal asymptotes. Explain your reasoning. Note: There are many correct answers.